Related papers: Quantitative Simulations by Matrices
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and…
We introduce and investigate a weighted propositional configuration logic over commutative semirings. Our logic is intended to serve as a specification language for software architectures with quantitative features. We prove an efficient…
The design of complex software systems usually lies in multiple coordinating components with an unknown number of instances. For such systems a main challenge is modelling efficiently their architecture that determines the topology and the…
Recent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a vector space of…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in…
Notions of simulation, among other uses, provide a computationally tractable and sound (but not necessarily complete) proof method for language inclusion. They have been comprehensively studied by Lynch and Vaandrager for nondeterministic…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of…
Simulators often provide the best description of real-world phenomena. However, they also lead to challenging inverse problems because the density they implicitly define is often intractable. We present a new suite of simulation-based…
We study the model-checking problem for a quantitative extension of the modal mu-calculus on a class of hybrid systems. Qualitative model checking has been proved decidable and implemented for several classes of systems, but this is not the…
We show that recent approaches of static analysis based on quantitative typing systems can be extended to programming languages with global state. More precisely, we define a call-by-value language equipped with operations to access a…
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
This paper investigates the problem of quantized matrix multiplication (MatMul), which has become crucial for the efficient deployment of large language models (LLMs). We consider a Generic MatMul setting, where both matrices must be…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
We present novel semiring semantics for abstract reduction systems (ARSs). More precisely, we provide a weighted version of ARSs, where the reduction steps induce weights from a semiring. Inspired by provenance analysis in database theory…
In this paper, we argue that simulation platforms enable a novel type of embodied spatial reasoning, one facilitated by a formal model of object and event semantics that renders the continuous quantitative search space of an open-world,…